Understanding Place Value in Regrouping

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Lesson Rubric and Worksheets
Student Sample One
Student Sample Two
Student Sample Three

Name: Gayle Hayes & Ginger Storey-Welch
Grade: 4
School: Colton-Pierrepont Central School

  1. Title/Context Of Learning Experience
    Learning Content/Introduction– In this learning experience, fourth grade students will demonstrate an understanding of place value to the hundred thousands’ place, and how it relates to addition and subtraction of whole numbers.Number Sense and Operations StrandStudents will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.Number Systems
    4.N.4 Identify and use: 10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand, 10 thousands = 1 ten thousand
    4.N.5 Recognize equivalent representations for numbers up to four digits and generate them by decomposing and composing numbers
    4.N.14 Use a variety of strategies to add and subtract numbers up to 10,000
    4.CM.1 Understand and explain how to organize their thought process

    Prior Knowledge
    In order to be successful with this learning experience, students need to:
    - Have a basic understanding of place value to 1,000.
    - Know basic computation skills.
    - Know how to use a computer.
    - Think critically and use logical reasoning.
    - Express their thoughts orally and in writing.

  2. Essential Question
    The children will be given hands-on opportunities to explore place value in performing operations. They will answer the essential question: How does our knowledge of place value help us understand adding and subtracting whole numbers to the hundred thousands’ column?
  3. Assessment Plan
    Two separate assessments for both addition and subtraction will be given. Students will explain in writing the processes used to add and subtract whole numbers through the thousands’ place, involving regrouping, especially across zeros with subtraction. They will use hands-on manipulatives, virtual manipulatives, and paper/pencil tasks to demonstrate their understanding of the processes. Also, a ten problem quiz on addition and subtraction to the hundred thousands’ column will be given (Worksheet 3). Teacher observation will also be used as an informal assessment. A rubric will be employed to evaluate the students’ understanding of place value in their writing and for the quiz.
  4. Procedure
    Day 1

    • Discussion of what students already know about place value.
    • Use hands-on manipulatives to build numbers to 100,000 and beyond, depending on ability, and practice decomposing and composing numbers. Place value blocks were used to build 4 digit numbers. For larger numbers, tri-colored place value mats were used to represent the ones’ period, the thousands’ period, the millions’ period, etc. Each period was labeled with an index card saying, “Ones’ Period,” etc. Commas on index cards separated the periods. Students were given stacks of magnetic number squares with the digits 0-9 and given directions like, “Build a 6 digit number with a three in the ten thousands’ place.” Other directions might be, “Build a 5 digit number which includes your 3……..What is the value of your 3?” (Answers would vary.) Teacher could also build a number and then ask students to rewrite the number in expanded form or to write the value of a particular digit.
    • On subsequent days, the stacks of magnetic squares with 0-9 were passed out (without the place value mats) to each student and used for quick 1-2 min. reviews of larger numbers. Instead of commas, students left a small space between periods. (The fact that the squares were magnetic is incidental.)

    Day 2

    Day 3

    • Build a million dots, as a class, using multiple copies of worksheet 1 and large mural paper.

    Day 4

    Day 5

    • Use the Smartboard to demonstrate subtraction using the virtual manipulatives. Teacher should create at least one problem with subtraction across zeros (see day 6): http://nlvm.usu.edu/en/nav/frames_asid_155_g_2_t_1.html
    • Students go to the computer lab and use http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html to build 4 digit numbers. This is a very short introduction on how to use the virtual manipulatives on their own.
    • Next in the computer lab, use http://nlvm.usu.edu/en/nav/frames_asid_155_g_2_t_1.html to practice subtraction using the virtual manipulatives. **(Students must regroup before attempting to subtract on the computer program.) **Remember to hit “Begin problem.”
    • Independent practice of subtraction: Use pencil and graph or lined paper to copy and solve each subtraction problem automatically generated by the computer. Next, verify each answer using the virtual manipulatives.

    Day 6

    • In the computer lab, use http://nlvm.usu.edu/en/nav/frames_asid_155_g_2_t_1.html to practice and understand subtraction across zeros, using the virtual manipulatives and worksheet 2. **(Students must regroup before attempting to subtract on the computer program.)
    • Students will write a paragraph demonstrating comprehension of regrouping in subtraction across zeros for at least one problem.

    Day 7

  5. Resources
    • http://www.mathlibs.org/
    • Links listed above
    • Paper, pencil
    • Dots – worksheet 1
    • Problem quiz - worksheet 3 and Rubric
    • Computer/internet access
    • Graph paper
    • Subtraction across zeros worksheet 2
  6. Instructional/Environmental Modifications
    Modifications are built into this lesson by the teacher being able to create problems individually for students as needed. Some students will need additional support with virtual manipulatives.
  7. Time Required
    1. Planning: Teachers need to preview websites.
    2. Time: Seven class periods, approximately 45 minutes long to implement the lessons.
    3. Assessment
      • Writing entries explaining addition and subtraction
      • Teacher observation
      • Quiz
  8. Reflection
    This learning experience which addresses the standard Number Sense and Operations, performance indicators 4.N.4, 4.N.5, 4.N.14, and 4.CM.1 was developed to ensure thorough understanding of place value in addition and subtraction.From implementing this lesson, we learned that it was valuable to have the students see the regrouping of virtual manipulatives. To see the tens “magically” break apart into ten ones and the hundreds “magically” break apart into ten tens, etc. was an effective teaching tool.

    Students thoroughly enjoyed in taking part in the various activities presented throughout the seven day lesson. We would definitely include this in future lesson planning.